Question

What is the slope of a line that is parallel to the line y =3/4 x + 2

Answer 1

The slope of a line parallel to y = 3/4 x + 2 is 3/4. Parallel lines have the same slope, so the answer is simply the coefficient of x in the original equation.

Step-by-step explanation:

The slope of a line is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on the line. This is often referred to as 'rise over run'. When looking at the equation of a straight line in the slope-intercept form, which is y = mx + b, the coefficient m represents the slope of the line. Hence, for a line parallel to y = 3/4 x + 2, the slope must be the same as the given line, which is 3/4.

Lines that are parallel have the same slope. This is because they have to maintain a consistent distance from each other, never intersecting. In the provided references, we see examples that describe how the slope remains the same along the entire length of a straight line and how parallel lines retain the same slope even if their y-intercepts differ.

Answer 2

Step-by-step explanation:

Given equation of line
`y=(3)/(4)x+2`

We have to find the slope of a line that is parallel to the given line.

Since any line parallel to the given line
`y=(3)/(4)x+2` will have same slope as that of given line

The general equation of line is given as y = mx + c

where. m is slope of line and c is y - intercept.

Thus for given equation of line
`y=(3)/(4)x+2`

Comparing , we get

slope is
`m=(3)/(4)`

Thus, any line with slope
`(3)/(4)` is parallel to the given line
`y=(3)/(4)x+2`